EE 7730 Image Enhancement Bahadir K Gunturk Image

EE 7730 Image Enhancement Bahadir K. Gunturk

Image Enhancement n n The objective of image enhancement is to process an image so that the result is more suitable than the original image for a specific application. There are two main approaches: q Image enhancement in spatial domain: Direct manipulation of pixels in an image n n q Point processing: Change pixel intensities Spatial filtering Image enhancement in frequency domain: Modifying the Fourier transform of an image Bahadir K. Gunturk 2

Image Enhancement by Point Processing n Intensity Transformation Bahadir K. Gunturk 3

Image Enhancement by Point Processing n Contrast Stretching Bahadir K. Gunturk 4

Image Enhancement by Point Processing n Contrast Stretching Bahadir K. Gunturk 5

Image Enhancement by Point Processing n Intensity Transformation Bahadir K. Gunturk 6

Image Enhancement by Point Processing n Intensity Transformation Bahadir K. Gunturk 7

Image Enhancement by Point Processing n Intensity Transformation Bahadir K. Gunturk 8

Image Enhancement by Point Processing n Gray-Level Slicing Bahadir K. Gunturk 9

Image Enhancement by Point Processing n Histogram 0 Bahadir K. Gunturk 255 12

Histogram Specification n Intensity mapping n Assume q T(r) is single-valued and monotonically increasing. q n The original and transformed intensities can be characterized by their probability density functions (PDFs) Bahadir K. Gunturk 13

Histogram Specification n The relationship between the PDFs is n Consider the mapping Cumulative distribution function of r Histogram equalization! Bahadir K. Gunturk 14

Image Enhancement by Point Processing n Histogram Equalization Bahadir K. Gunturk 15

Image Enhancement by Point Processing n Histogram Equalization Example Intensity Number of pixels 0 1 2 3 10 20 12 8 Intensity Number of pixels 0 1 2 0 10 0 Bahadir K. Gunturk 4 0 5 0 6 0 7 0 3 4 5 6 0 20 0 12 7 8 16

Image Enhancement by Point Processing n Histogram Equalization Bahadir K. Gunturk 17

Histogram Specification n Intensity mapping n Assume q T(r) is single-valued and monotonically increasing. q n The original and transformed intensities can be characterized by their probability density functions (PDFs) Bahadir K. Gunturk 18

Histogram Specification n The relationship between the PDFs is n Consider the mapping Cumulative distribution function of r Histogram equalization! Bahadir K. Gunturk 19

Histogram Specification n Example Assume Equalization mapping is then found to be The inverse mapping is r must be between 0 and 1 Bahadir K. Gunturk 20

Histogram Specification n Example Check out the new PDF is Bahadir K. Gunturk 21

Histogram Specification n Assume we have a desired PDF n Let the following be the equalization mappings n Then, the desired mapping is Bahadir K. Gunturk 22

Histogram Specification Bahadir K. Gunturk 23

Histogram Specification Bahadir K. Gunturk 24

Histogram Specification Bahadir K. Gunturk 25

Histogram Specification Bahadir K. Gunturk 26

Local Histogram Processing n Histogram processing can be applied locally. Bahadir K. Gunturk 27

Image Subtraction The background is subtracted out, the arteries appear bright. Bahadir K. Gunturk 28

Image Averaging Corrupted image Original image Noise Assume n(x, y) a white noise with mean=0, and variance If we have a set of noisy images The noise variance in the average image Bahadir K. Gunturk is 29

Image Averaging Bahadir K. Gunturk 30

Spatial Filtering A low-pass filter A high-pass filter Bahadir K. Gunturk 31

Spatial Filtering n Median Filter Sort: (10 10 10 20 25 75 85 90 100) n Example Original signal: 100 100 10 10 10 Noisy signal: 100 103 100 10 9 10 11 10 Filter by [ 1 1 1]/3: 101 70 40 10 10 10 Filter by 1 x 3 median filter: 100 100 10 10 Bahadir K. Gunturk 32

Spatial Filtering n n n Median filters are nonlinear. Median filtering reduces noise without blurring edges and other sharp details. Median filtering is particularly effective when the noise pattern consists of strong, spikelike components. (Salt-andpepper noise. ) Bahadir K. Gunturk 33

Spatial Filtering Original 3 x 3 averaging filter Bahadir K. Gunturk Salt&Pepper noise added 3 x 3 median filter 34

Spatial Filtering Bahadir K. Gunturk 35

Spatial Filtering n Gradient Operators q q q Averaging of pixels over a region tends to blur detail in an image. As averaging is analogous to integration, differentiation can be expected to have the opposite effect and thus sharpen an image. Gradient operators (first-order derivatives) are commonly used in image processing applications. Bahadir K. Gunturk 36

Spatial Filtering n Gradient Operators These are called the Sobel operators Bahadir K. Gunturk 37

Spatial Filtering n Laplacian Operators q Laplacian operators are second-order derivatives. Bahadir K. Gunturk 38

Spatial Filtering Bahadir K. Gunturk 39

Spatial Filtering n High-boost or high-frequency-emphasis filter q Sharpens the image but does not remove the low-frequency components unlike high-pass filtering Bahadir K. Gunturk 40

Spatial Filtering n High-boost or high-frequency-emphasis filter q q High pass = Original – Low pass High boost = (K)(Original) – Low pass = (K-1)(Original) + Original – Low pass = (K-1)(Original) + High pass When K=1, High boost = High pass When K>1, Part of the original is added back to the highpass result. Bahadir K. Gunturk 41